The value of $^{15}C_3 + ^{15}C_{13}$ is

Let $A = \{a_1, a_2, a_3, ..., a_n\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of $A$ are formed independently. The number of ways in which these subsets can be formed such that $(P - Q)$ contains exactly $2$ elements is:

In an election there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?

The number of integers greater than $6000$ that can be formed using the digits $3, 5, 6, 7,$ and $8$ without repetition is:

Find the total number of $9$ digit numbers which have all the digits different.

If the four-letter words (need not be meaningful) are to be formed using the letters from the word "$MEDITERRANEAN$" such that the first letter is $R$ and the fourth letter is $E,$ then the total number of all such words is